Applications of Derivatives: Optimization

General Procedure

1. Identify the variable you want to optimize, for example, you want to maximize area, A.

2. Identify the independent variable. For example, what is area going to be a function of? length and height, x and y?

3. Now you need an equation for A(x). It may be obvious or you may need a sketch to come up with the equation. Follow the steps we went over for problem solving.

4. Take the derivative, dA/dx.

5. Set it equal to zero and solve for x.

6. Check to see if this is a minimum or maximum by taking the second derivative. You can also look at a plot of the equation for this.

7. If it’s A you are solving for, plug x back into your original equation.